Seminars
View all Seminars | Download ICal for this eventInstance-dependent Sample Complexity Bounds for Zero-sum Matrix Games
Series: Bangalore Theory Seminars
Speaker: Arnab Maiti, University of Washington
Date/Time: May 12 11:00:00
Location: Microsoft Teams link - Online (See Teams link below)
Abstract:
We study the sample complexity of identifying an approximate equilibrium for two-player zero-sum n?2 matrix games. That is, in a sequence of repeated game plays, how many rounds must the two players play before reaching an approximate equilibrium (e.g., Nash)? We derive instance-dependent bounds that define an ordering over game matrices that captures the intuition that the dynamics of some games converge faster than others. Specifically, we consider a stochastic observation model such that when the two players choose actions i and j, respectively, they both observe each others played actions and a stochastic observation Xij such that EXij = Aij. To our knowledge, our work is the first case of instance-dependent lower bounds on the number of rounds the players must play before reaching an approximate equilibrium in the sense that the number of rounds depends on the specific properties of the game matrix A as well as the desired accuracy. We also prove a converse statement: there exist player strategies that achieve this lower bound
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Microsoft Teams link:
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We are grateful to the Kirani family for generously supporting the theory seminar series
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Hosts: Rameesh Paul, Rahul Madhavan, Aditya Subramanian and Aditya Abhay Lonkar